Quasicontinuum method extended to irregular lattices

Abstract

The quasicontinuum (QC) method, originally proposed by Tadmor, Ortiz and Phillips in 1996, is a computational technique that can efficiently handle regular atomistic lattices by combining continuum and atomistic approaches. In the present work, the QC method is extended to irregular systems of particles that represent a heterogeneous material. The paper introduces five QC-inspired approaches that approximate a discrete model consisting of particles connected by elastic links with axial interactions. Accuracy is first checked on simple examples in two and three spatial dimensions. Computational efficiency is then assessed by performing three-dimensional simulations of an L-shaped specimen with elastic-brittle links. It is shown that the QC-inspired approaches substantially reduce the computational cost and lead to macroscopic crack trajectories and global load-displacement curves that are very similar to those obtained by a fully resolved particle model.

Comparative study of multiscale computational strategies for materials with discrete microstructures

“…Additional research focused on goal-oriented adaptivity [2,46], a meshless QC method [40], or an energy-based variational formulation for regular lattices with plasticity [60] and localized damage [62,61]. Recently, the QC method was also extended to irregular lattices [50] or polymer networks [31]. A generalization to metallic lattice materials was introduced in [21], where different finite element shape functions are used for different types of lattice nodes.…”

Modelling of Crack Propagation: Comparison of Discrete Lattice System and Cohesive Zone Model

“…In each time step, the minimization problem of Eq. (1) is solved to obtain a local minimum that satisfies the energy balance (6) which equates the internally stored energy V(q) − V(q 0 ) plus the dissipated energy…”

Adaptive Quasicontinuum Simulation of Elastic-Brittle Disordered Lattices

“…Since that time, the QC method has been widely used and extended to applications for a variety of materials represented by regular lattices [2]. An extension of the QC method to irregular lattices has recently been developed by the authors [3].…”

“…Afterwards, the material parameters of 2D elements can be identified as isotropic, orthotropic, or arbitrarily anisotropic. Different homogenization procedures for disordered lattices with normal interactions are described in [3].…”